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arXiv · 1512.01702

On Bohr sets of integer valued traceless matrices

Alexander Fish
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Abstract

In this paper we show that any Bohr-zero non-periodic set $B$ of traceless integer valued matrices, denoted by $\Lambda$, intersects non-trivially the conjugacy class of any matrix from $\Lambda$. As a corollary, we obtain that the family of characteristic polynomials of $B$ contains all characteristic polynomials of matrices from $\Lambda$. The main ingredient used in this paper is an equidistribution result for an $SL_d(\mathbf{Z})$ random walk on a finite-dimensional torus deduced from Bourgain-Furman-Lindenstrauss-Mozes work.

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Alexander Fish. 2015-12-05. On Bohr sets of integer valued traceless matrices. https://arxiv.org/abs/1512.01702

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